Proxy-SU(3) symmetry in heavy deformed nuclei

Abstract

Background: Microscopic calculations of heavy nuclei face considerable difficulties due to the sizes of the matrices that need to be solved. Various approximation schemes have been invoked, for example by truncating the spaces, imposing seniority limits, or appealing to various symmetry schemes such as pseudo-SU(3). This paper proposes a new symmetry scheme also based on SU(3). This proxy-SU(3) can be applied to well-deformed nuclei, is simple to use, and can yield analytic predictions. Purpose: To present the new scheme and its microscopic motivation, and to test it using a Nilsson model calculation with the original shell model orbits and with the new proxy set. Method: We invoke an approximate, analytic, treatment of the Nilsson model, that allows the above vetting and yet is also transparent in understanding the approximations involved in the new proxy-SU(3). Results: It is found that the new scheme yields a Nilsson diagram for well-deformed nuclei that is very close to the original Nilsson diagram. The specific levels of approximation in the new scheme are also shown, for each major shell. Conclusions: The new proxy-SU(3) scheme is a good approximation to the full set of orbits in a major shell. Being able to replace a complex shell model calculation with a symmetry-based description now opens up the possibility to predict many properties of nuclei analytically and often in a parameter-free way. The new scheme works best for heavier nuclei, precisely where full microscopic calculations are most challenged. Some cases in which the new scheme can be used, often analytically, to make specific predictions, are shown in a subsequent paper.

arXiv comment24 pages, 6 figures, 15 tables

References in corpus (6)

• Pseudo-spin as a Relativistic Symmetry
• Spherical Shell Model description of rotational motion
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Emergent Collectivity in Nuclei and Enhanced Proton-Neutron Interactions
• The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies and the Nilsson model

Cited by in corpus (31)

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• The proxy-SU(3) symmetry in atomic nuclei
• Proxy-SU(3) symmetry in the shell model basis
• Islands of shape coexistence from single-particle spectra in covariant density functional theory
• Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
• Signatures for shape coexistence and shape/phase transitions in even-even nuclei
• Islands of shape coexistence: theoretical predictions and experimental evidence
• Triaxial rotor modes in finite-N boson systems
• B(E2) anomaly and triaxial deformation in the interacting boson model
• Symmetry Restoration in Mixed-Spin Paired Heavy Nuclei
• Proxy-SU(3) symmetry in heavy nuclei: Prolate dominance and prolate-oblate shape transition
• Signatures of shape phase transitions in krypton isotopes based on relativistic energy density functionals
• Proxy-$SU(4)$ symmetry in A=60-90 region
• B(E2) anomaly and triaxial deformation within a two-fluid SU(3) symmetry
• A Semimicroscopic Algebraic Cluster Model for Heavy Nuclei
• Understanding Xe isotopes near $A=130$ through the prolate-oblate shape phase transition
• New Procedure for Evaluation of U(3) Coupling and Recoupling Coefficients
• Proxy-SU(3): A symmetry for heavy nuclei
• Semi-microscopic construction of multi-$\alpha$ cluster spaces
• Coupling and Recoupling Coefficients for Wigner's U(4) Supermultiplet Symmetry
• Magic numbers for shape coexistence
• Prolate dominance and prolate-oblate shape transition in the proxy-SU(3) model
• Quadrupole-Octupole Residual Interaction in the Proxy-$SU(3)$ Scheme
• Foundations of the proxy-SU(3) symmetry in heavy nuclei
• Parameter-independent predictions for shape variables of heavy deformed nuclei in the proxy-SU(3) model
• Shell-model representations of the microscopic version of the Bohr-Mottelson collective model
• A symmetry for heavy nuclei: Proxy-SU(3)
• Connection between Elliott SU(3) and spherical shell model bases
• Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme